Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int me = 100025;
int N;
long double H;
int main(int argc, const char* argv[]) {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> N >> H;
  long double last = sqrt(H * H / (long double)N);
  cout.precision(10);
  cout << fixed << last << " ";
  for (int i = 2; i < N; i++) {
    long double low = last, high = H, mid, best = high;
    for (int _ = 0; _ < 50; _++) {
      mid = (low + high) / 2.;
      if (mid * mid >= last * last * (long double)(i) / (long double)(i - 1)) {
        best = mid;
        high = mid;
      } else {
        low = mid;
      }
    }
    cout.precision(10);
    cout << fixed << best;
    if (i < N - 1) cout << " ";
    last = best;
  }
  cout << endl;
  return 0;
}